{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T01:21:21Z","timestamp":1698369681115},"reference-count":14,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":7802,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1985,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The problem of computing the SKT reliability, the probability that a source <jats:italic>s<\/jats:italic> can send communication to a specified set of terminals <jats:italic>K<\/jats:italic> \u2282 <jats:italic>V<\/jats:italic> in a probabilistic digraph <jats:italic>D<\/jats:italic> = (V,E) is considered. For general digraphs, this problem is known to be NP\u2010hard and it is helpful to consider schemes that can decompose the problem into a number of smaller problems. A non\u2010separable digraph is 2\u2010connected if it contains a separation pair, a pair of nodes whose removal disconnects the digraph. Such a digraph can be partitioned into two or more segments. It is shown that at least one of these segments can be replaced by a simpler structure; this replacement results in an exact reliability preserving reduction. The proposed reduction scheme is general and is applicable to all digraphs containing a separation pair; earlier methods could only handle special cases. For a class of digraphs, called BSP digraphs, such a reduction is always admissible and the SKT reliability can be computed in time O(\u2223<jats:italic>E<\/jats:italic>\u2223). A digraph is a BSP digraph if its underlying undirected graph is series\u2010parallel. A BSP digraph can be cyclic or acyclic. No polynomial\u2010time algorithms were previously known for this class of digraphs.<\/jats:p>","DOI":"10.1002\/net.3230150209","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T19:20:37Z","timestamp":1178911237000},"page":"239-256","source":"Crossref","is-referenced-by-count":15,"title":["Network reliability analysis using 2\u2010connected digraph reductions"],"prefix":"10.1002","volume":"15","author":[{"given":"Avinash","family":"Agrawal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Satyanarayana","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.32.3.493"},{"key":"e_1_2_1_3_2","volume-title":"Source to K terminal reliability analysis of rooted communication networks, ORC 83\u20102","author":"Agrawal A.","year":"1983"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100206"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/0113027"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_7_2","unstructured":"J. N.Hagstrom Combinatoric Tools for Computing Network Reliability Ph. D. Thesis University of California Berkeley (1980)."},{"key":"e_1_2_1_8_2","first-page":"581","volume-title":"Reliability and Fault Tree Analysis","author":"Murchland J. D.","year":"1975"},{"key":"e_1_2_1_9_2","first-page":"133","volume-title":"Reliability and Fault Tree Analysis","author":"Rosenthal A.","year":"1975"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1982.5221215"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230130107"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"A.Satyanarayana andR. K.Wood Polygon\u2010to\u2010chain reductions and network reliability Technical Report ORC 82\u20104 Operations Research Center University of California Berkeley (1982) (SIAM J. Computing to appear).","DOI":"10.21236\/ADA116276"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230070304"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0211023"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1137\/0208032"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230150209","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230150209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T21:23:07Z","timestamp":1697836987000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230150209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,6]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1985,6]]}},"alternative-id":["10.1002\/net.3230150209"],"URL":"https:\/\/doi.org\/10.1002\/net.3230150209","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,6]]}}}